Multiplication algorithm: Difference between revisions

Revision as of 22:38, 10 January 2014

Revision as of 11:10, 11 January 2014

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Describing the steps explicitly:

* There are two columns: a "doubling" column and a "halving" column. In this case, 11 has been chosen as the start of the "halving" column, but the method works when the opposite choice is made.

* 11 and 3 are written at the top

* 11 is halved (5.5) and 3 is doubled (6). The fractional portion is discarded (5.5 becomes 5).

* 5 is halved (2.5) and 6 is doubled (12). The fractional portion is discarded (2.5 becomes 2). The figure in the left ("halving") column (2) is '''even''', so the figure in the right ("doubling") column (12) is discarded.

* 2 is halved (1) and 12 is doubled (24).

* All not-scratched-out values in the "doubling" column are summed: 3 + 6 + 24 = 33.

* Stop reducing it to "all non-scratched-out-values" because that on its own means you'd add 11+5+2+1+3+6+24. You HAVE to specify that it's only ONE COLUMN which is added. Otherwise, how will anyone know what you mean?

The method works because multiplication is [[distributivity|distributive]], so:

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\end{align}

</math>

In practice, less work is done if the smaller number (3 in the aobve example) is halved and the larger number is doubled. This leads to a shorter table.

A more complicated example, using the figures from the earlier examples (23,958,233 and 5,830):